The PA news agency understands Zaha was subjected to the abuse in a series of posts on Twitter.
The abuse, however, was not anything connected to Zaha playing in the Eagles’ last Premier League match at West Ham before the international break.
After being made aware of the posts by the player himself, Palace took swift action to report them to both the social media platform and also the appropriate authorities.
PA understands the club are determined to identify the individual concerned. If found to be a Palace supporter or season-ticket holder, they would be dealt with by club disciplinary procedures – which could result in a ban from Selhurst Park.
A statement read: “Crystal Palace Football Club has taken action after one of our players, Wilfried Zaha, has again been subjected to racist abuse on social media.
“We will not tolerate this behaviour being directed at any of our players and will fully support them in dealing with such incidents.
“Any action we can take unilaterally as a club will be taken immediately and we will also seek co-operation from other clubs where relevant. Following that we will pursue the matter criminally with the full force of whatever the law allows.”
Anti-discrimination campaigners Kick It Out backed Palace’s stance.
A statement read: “We fully support the response from Crystal Palace to the latest incident of vile racist abuse directed at Wilfried Zaha online.
“It’s extremely frustrating to continue to witness hatred on social platforms.
“While recognising it is a wider social issue, we utterly condemn the language used and demand that the platforms come forward with appropriate actions.”
Ivory Coast international Zaha saw his summer disrupted by transfer speculation while he was away at the Africa Cup of Nations.
Having seen a move fail to materialise ahead of the deadline, with Arsenal and Everton both reported to be potential suitors, Zaha remained at Selhurst Park.
And Palace sit sixth in the Premier League table during the international break after their 2-1 win against West Ham at the London Stadium.
Zaha had previously spoken out against online racist abuse he received last season.
The forward was targeted following last October’s 2-2 Premier League draw with Arsenal, during which he won a penalty after going down under Granit Xhaka’s challenge.
Zaha had taken to social media to stand up for himself following the Arsenal game, and subsequently revealed in a post on his Instagram story the abuse had escalated.
He wrote: “For all the people taking it one step further and being racist and wishing death on my family I wish you and your families the best too x p.s my life is still very good despite your hate.”